1. Numerical simulation to predict the final
shape of PM HIP components
IWM / IAPK Institute, RWTH Aachen University
Augustinerbach 4, 52062 Aachen Germany
Chung Van Nguyen
Email: c.nguyenvan@iwm.rwth-aachen.de
nvchungdhgt@yahoo.com
Phone: +49 241 80 96291
Mobile: +49 176 82106600

2. 2
Content
1 Introduction
2 Densification models
3 Implementation
4 Simulation results
5 Anisotropic shrinkage of PM-HIP components

3. 3
Introduction
The powder HIP production processes

4. 4
Courtesy of KEG GmbH
Anisotropic shrinkage
This problem leads to higher costs for post
processing and longer delivery time.
In order to improve technically and make it
cost efficient, NNS HIP parts must be
produced from the first shot with the
minimal geometrical allowances.
Thus, the main motivation is to create a
HIP simulation tool to replace the “trial and
error” methodology.
Courtesy of IWM

5. 5
Content
1 Introduction
2 Densification models
3 Implementation
4 Simulation results
5 Anisotropic shrinkage of PM-HIP components

6. 6
Simulation approach
constitutive equations
𝜀 = 𝜀 𝑒𝑙
+ 𝜀 𝑖𝑛𝑒𝑙
+ 𝜀 𝑡ℎ
𝜀 𝑖𝑛𝑒𝑙
= 𝜀
𝑝𝑙
+ 𝜀 𝑐𝑟
Modified from Von Mises yield condition

7. 7
d𝜀𝑖𝑗
𝑝
= dλ
𝜕f1
𝜕σ𝑖𝑗
dλ =
𝜕𝑓1
𝜕𝜎𝑖𝑗
∙ 𝑪𝒊𝒋𝒌𝒍
𝒆𝒍
d𝜀𝑖𝑗
𝜕𝑓1
𝜕𝜎𝑖𝑗
∙ 𝑪𝒊𝒋𝒌𝒍
𝒆𝒍 𝜕𝑓1
𝜕𝜎𝑖𝑗
+
𝜕𝑓1
𝜕𝜌
∙ 𝜌
𝜕𝑓1
𝜕𝜎𝑖𝑗
𝛿 𝑘𝑘 −
𝜕𝑓1
𝜕𝑝
2
3
𝜕𝑓1
𝜕𝜎𝑖𝑗
∙
𝜕𝑓1
𝜕𝜎𝑖𝑗
1 2
The plastic deformation calculation bases on the consistency condition, associated flow rule
and the mass conservation principle.
𝑛𝑖𝑗 =
𝜕f1
𝜕σ𝑖𝑗
𝜕𝑓1
𝜕𝜌
=
𝑛∙𝜌 𝑛−1 𝐽2−
1
3
∙𝑛∙𝜌 𝑛−1 𝐼1
2
2𝜎 𝑒𝑞1
1 2 − ℎ ∙ 𝑚 ∙ 𝜌 𝑚−1
− 𝜎0 ∙ 𝑘 ∙ 𝜌 𝑘−1
)
𝜕𝑓1
𝜕𝑝
= − ℎ ∙ 𝜌 𝑚 ,
= −ℎ1 ∙ 𝜌 𝑚
Constitutive equation:
plasticity model
𝑓1 𝜎𝑖𝑗, 𝜌, 𝑃 = 𝜎𝑒𝑞1 𝜌) − 𝑟1 𝜌, 𝑃 − 𝜎 𝑦 𝜌 = 0 1
2
3
4
5

8. 8
𝜀 𝑖𝑛𝑒𝑙
= 𝜀 𝑐𝑟
= 𝜀 𝑐𝑟1
+ 𝜀 𝑐𝑟2
𝜀𝑖𝑗
𝑐𝑟
= 𝜀𝑖𝑗
𝑐𝑟2
= ex p −
𝑄
𝑅𝑇
)𝜎𝑒𝑞2
𝑁 𝑛−1 3𝑐 𝜌
2
𝑆𝑖𝑗 + 𝑓 𝜌 𝐼1 𝛿𝑖𝑗
𝜀𝑖𝑗
𝑐𝑟
= 𝜀𝑖𝑗
𝑐𝑟2
+ 𝜀𝑖𝑗
𝑐𝑟2
= ex p −
𝑄
𝑅𝑇
)𝜎𝑒𝑞2
𝑁 𝑛−1
1 + 𝑚 −
1
ex p 𝑘𝜀𝑖𝑗
𝑐𝑟
𝑁 𝑛−1
3𝑐 𝜌
2
𝑆𝑖𝑗 + 𝑓 𝜌 𝐼1 𝛿𝑖𝑗
Constitutive equation:
viscoplasticity model
1
2
3

9. 9
Content
1 Introduction
2 Densification models
3 Implementation
4 Simulation results
5 Anisotropic shrinkage of PM-HIP components

10. 10
Implementation in UMAT Subroutine

11. 11
Different material models
Table 1: Different constitutive equation used for HIP simulation
Model’s name Characteristic
Plastic Elastoplastic 𝜀𝑖𝑗
𝑖𝑛𝑒𝑙
= 𝜀𝑖𝑗
𝑃𝑙
Viscoplastic Elastoviscoplastic 𝜀𝑖𝑗
𝑖𝑛𝑒𝑙
= 𝜀𝑖𝑗
𝑐𝑟2
Combined model No.1 Elasto-plasto-viscoplastic 𝜀𝑖𝑗
𝑖𝑛𝑒𝑙
= 𝜀𝑖𝑗
𝑝𝑙
+ 𝜀𝑖𝑗
𝑐𝑟
= 𝜀𝑖𝑗
𝑝𝑙
+ 𝜀𝑖𝑗
𝑐𝑟2
Combined model No.2 Elasto-plasto-viscoplastic 𝜀𝑖𝑗
𝑖𝑛𝑒𝑙
= 𝜀𝑖𝑗
𝑝𝑙
+ 𝜀𝑖𝑗
𝑐𝑟
= 𝜀𝑖𝑗
𝑝𝑙
+ 𝜀𝑖𝑗
𝑐𝑟1
+ 𝜀𝑖𝑗
𝑐𝑟2

12. 12
Content
1 Introduction
2 Densification models
3 Implementation
4 Simulation results
5 Anisotropic shrinkage of PM-HIP components

13. 13
Simulation results of test capsules
Combined models give the best shape prediction with the error below 1,5%

14. 14
Content
1 Introduction
2 Densification models
3 Implementation
4 Simulation results
5 Anisotropic shrinkage of PM-HIP components

15. 15
Shape and size
Thickness, material properties
Number of weldlines, location
of welded joints
Inhomogeneous powder
distribution
Powder particle size, size
distribution can be different
Temperature, pressure
Temperature gradient
Capsule Powder prior to HIP HIP cycle
PM HIP Production process

16. 16
With a homogeneous initial powder distribution with an inhomogeneous initial powder distribution
Influence of capsule thickness

17. 17
Influence of initial
powder distribution
Relative density distribution was determined from experiment based on Image Analysis

18. 18
Influence of initial powder
distribution
Homogeneous initial powder distribution Powder distribution from experiment
Bending due to the influence of inhomogeneous powder distribution

19. 19
Influence of powder particle size
distribution
Table 5-4: Powder particle size fraction of three used powders
Fraction F1 F2 F3 F4 F5 F6
Micron >250 250-212 212-125 125-100 45-100 <45
Powder (P1) 17 16 15 10 28 14
Powder (P2) 17 16 15 10 28 0
Powder (P3) 50 0 20 5 10 15

20. 20
Influence of powder particle size
distribution
Influence of different powder distribution distribution
Final shape of capsules which used different powder fractions as shown in the previous slide

21. 21
Homogeneous
Powder dis.
Powder dis.
Taken from IA
Capsule No.1 Comparision of
the final shape
Influence of temperature
gradient
Bending due to the influence of temperature gradient

22. 22
Optimize capsule’s shape and size

23. Thank you very much for your attention
Nguyen Van Chung
IAPK – Institut für Anwendungstechnik Pulvermetallurgie und Keramik
an der RWTH Aachen e.V.
Augustinerbach 4
52062 Aachen
www.iapk.rwth-aachen.de